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Файл:4 семестр (2 курс)лала / Физика / Кратко / 18 Спин. Квантовые числа
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!?8= ( A?8=>2K9 <><5=B) MB> :20=B>20O 25;8G8=0, =5 8<5NI0O :;0AA8G5A:>3> 0=0;>30. = O2;O5BAO =5>BJ5<;5<K< A2>9AB2>< M;5:B@>=0 8 4@C38E M;5<5=B0@=KE G0AB8F ( B5<0 3 2 ) ?>4>1=> B><C, :0: >=8 8<5NB <0AAC, 0 70@O65==K5 G0AB8FK 5I5 8 70@O4. !?8= E0@0:B5@87C5B 2=CB@5==55 A2>9AB2> :20=B>2>9 G0AB8FK, A2O70==>5 A =0;8G85< C =55 4>?>;=8B5;L=>9 AB5?5=8 A2>1>4K.
>4C;L A?8=0 ( A>1AB25==>3> <5E0=8G5A:>3> <><5=B0 8<?C;LA0) M s G0AB8FK >?@545;O5BAO ?> 70:>=0< :20=B>2>9 B5>@88 8 4>;65= 1KBL :20=B>20= ?> 70:>=C M = h ( A :@5AB><) * [ :>@5=L( s * ( s + 1 ) ) ] , 345 s A?8=>2>5 :20=B>2>5 G8A;> ( G0AB> =07K20NB A?8=><) . >B;8G85 >B
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@>5:F8O M [ 8=45:A] s z A?8=0 =0 >AL Z B0:65 4>;6=0 1KBL :20=B>20=0:
M [ 8=45:A] s z = h ( A :@5AB><) m [ 8=45:A] s , m [ 8=45:A] s = - s , - s + 1 , . . . , s - 1 , s , 345 m s <03=8B=>5 A?8=>2>5 ( =07K20NB B0:65 ?@>AB> A?8=>2K<) :20=B>2>5 G8A;> G8A;> 2>7<>6=KE ?@>5:F89 M [ 8=45:A] s z , A>>B25BAB2CNI8E 40==><C 7=0G5=8N s .
C45< >1>7=0G0BL >@18B0;L=K9 <03=8B=K9 <><5=B p [ 8=45:A] m :0: [ <N] [ 8=45:A] l , 0 >@18B0;L=K9 <5E0=8G5A:89 <><5=B L [ 8=45:A] e 1C:2>9 [ 8=45:A] l .
>4C;L >@18B0;L=>3> <5E0=8G5A:>3> <><5=B0 M;5:B@>=0 <>6=> >?@545;8BL ?> D>@<C;5 [ 8=45:A] l = h ( A :@5AB><) * [ :>@5=L( l * ( l + 1 ) ) ] ,
345 l = 0 , 1 , 2 , . . . >@18B0;L=>5 :20=B>2>5 G8A;> M;5:B@>=0.
@>5:F8O >@18B0;L=>3> <5E0=8G5A:>3> <><5=B0 M;5:B@>=0 =0 =5:>B>@>5 =0?@02;5=85 Z A>3;0A=> D>@<C;5 >?@545;O5BAO 2K@065=85< M [ 8=45:A] l z = m [ 8=45:A] l * h ( A :@5B><) , 345 m l = - l , - l + 1 , . . . , l - 1 , l <03=8B=>5 :20=B>2>5 G8A;> M;5:B@>=0. !;54>20B5;L=>, ?@8 m [ 8=45:A] l <
!?8= ( A?8=>2K9 <><5=B) MB> :20=B>20O 25;8G8=0, =5 8<5NI0O :;0AA8G5A:>3> 0=0;>30. = O2;O5BAO =5>BJ5<;5<K< A2>9AB2>< M;5:B@>=0 8 4@C38E M;5<5=B0@=KE G0AB8F ( B5<0 3 2 ) ?>4>1=> B><C, :0: >=8 8<5NB <0AAC, 0 70@O65==K5 G0AB8FK 5I5 8 70@O4. !?8= E0@0:B5@87C5B 2=CB@5==55 A2>9AB2> :20=B>2>9 G0AB8FK, A2O70==>5 A =0;8G85< C =55 4>?>;=8B5;L=>9 AB5?5=8 A2>1>4K.
>4C;L A?8=0 ( A>1AB25==>3> <5E0=8G5A:>3> <><5=B0 8<?C;LA0) M s G0AB8FK >?@545;O5BAO ?> 70:>=0< :20=B>2>9 B5>@88 8 4>;65= 1KBL :20=B>20= ?> 70:>=C M = h ( A :@5AB><) * [ :>@5=L( s * ( s + 1 ) ) ] , 345 s A?8=>2>5 :20=B>2>5 G8A;> ( G0AB> =07K20NB A?8=><) . >B;8G85 >B
:20=B>2KE G8A5; l 8 m G8A;> s <>65B 1KBL :0: F5;K<, B0: 8 ?>;CF5;K<.
@>5:F8O M [ 8=45:A] s z A?8=0 =0 >AL Z B0:65 4>;6=0 1KBL :20=B>20=0:
M [ 8=45:A] s z = h ( A :@5AB><) m [ 8=45:A] s , m [ 8=45:A] s = - s , - s + 1 , . . . , s - 1 , s , 345 m s <03=8B=>5 A?8=>2>5 ( =07K20NB B0:65 ?@>AB> A?8=>2K<) :20=B>2>5 G8A;> G8A;> 2>7<>6=KE ?@>5:F89 M [ 8=45:A] s z , A>>B25BAB2CNI8E 40==><C 7=0G5=8N s .
C45< >1>7=0G0BL >@18B0;L=K9 <03=8B=K9 <><5=B p [ 8=45:A] m :0: [ <N] [ 8=45:A] l , 0 >@18B0;L=K9 <5E0=8G5A:89 <><5=B L [ 8=45:A] e 1C:2>9 [ 8=45:A] l .
>4C;L >@18B0;L=>3> <5E0=8G5A:>3> <><5=B0 M;5:B@>=0 <>6=> >?@545;8BL ?> D>@<C;5 [ 8=45:A] l = h ( A :@5AB><) * [ :>@5=L( l * ( l + 1 ) ) ] ,
345 l = 0 , 1 , 2 , . . . >@18B0;L=>5 :20=B>2>5 G8A;> M;5:B@>=0.
@>5:F8O >@18B0;L=>3> <5E0=8G5A:>3> <><5=B0 M;5:B@>=0 =0 =5:>B>@>5 =0?@02;5=85 Z A>3;0A=> D>@<C;5 >?@545;O5BAO 2K@065=85< M [ 8=45:A] l z = m [ 8=45:A] l * h ( A :@5B><) , 345 m l = - l , - l + 1 , . . . , l - 1 , l <03=8B=>5 :20=B>2>5 G8A;> M;5:B@>=0. !;54>20B5;L=>, ?@8 m [ 8=45:A] l <